9The layout of an integrated circuit (lC) is the process of assigning geometric shape, size and position to the components (transistors and connections) used in its fabrication. Since the number of components in modem ICs is enormous, computer- aided-design (CAD) programs are required to automate the difficult layout process. Prior CAD methods are inexact or limited in scope, and produce layouts whose area, and consequently manufacturing costs, are larger than necessary. This book addresses the problem of minimizing exactly the layout area of an important class of basic IC structures called CMOS cells. First, we precisely define the possible goals in area minimization for such cells, namely width and height minimization, with allowance for area-reducing reordering of transistors. We reformulate the layout problem in terms of a graph model and develop new graph-theoretic concepts that completely characterize the fundamental area minimization problems for series-parallel and nonseries-parallel circuits. These concepts lead to practical algorithms that solve all the basic layout minimization problems exactly, both for a single cell and for a one-dimensional array of such cells. Although a few of these layout problems have been solved or partially solved previously, we present here the first complete solutions to all the problems of interest.